When a new card is drawn, it would be nice if either this is slower, or the card highlighted in your hand. Alternatively, the history of moves could show what card was drawn (to you only obviously). I find that in larger hands, I can't easily tell which new card I've just drawn.

Absolutely agree. Or have an animation.With larger hands the cards tend to re-align for some reason (this seems to be a generel problem with the BGA stock structure), and then it's impossible to tell where a new card has appeared.